Vice President Biden is doubling down on watchdog groups and others who are saying he made misleading remarks in a speech earlier this week regarding the Romney-Ryan rescue plan for Medicare – daring reporters to “fact check me.”

Biden put down the challenge during a speech Saturday, after saying as he did during his acceptance speech Thursday at the Democratic National Convention that GOP presidential nominee Mitt Romney and running mate Rep. Paul Ryan’s plan would cut benefits immediately for 30 million seniors already collecting Medicare.

“I say to the press, fact check me,” a smiling Biden said to applause at a rally in Zanesville, Ohio,

The Romney Campaign took up the challenge within hours.

“Today, Vice President Biden said that he should be fact checked, and we agree,” said Romney campaign spokeswoman Amanda Henneberg. “The vice president knowingly and deliberately leveled false and discredited attacks. This is further proof that the Obama Campaign is unable and unwilling to talk honestly or substantively about the most important issues driving the country."

More On This...

"In an attempt to distract from President Obama’s failed record, including unemployment remaining over 8 percent, labor force participation falling to three-decade lows, and our national debt passing $16 trillion, Vice President Biden is once again advancing fabricated and disproven attacks on Mitt Romney and Paul Ryan," Henneberg added.

The Romney campaign also on Saturday released a statement with fact-checks on statements Biden made relating to Romney's tax and Medicare plans, and claims from Biden that Romney shipped jobs overseas.

Biden and President Obama made other statements in their convention speeches on such topics as unemployment and Medicare that fact-checkers said also appear to be inaccurate or at least misleading.

Among the questionable remarks were Biden's argument that "after the worst job loss since the Great Depression we created 4.5 million private sector jobs in the past 29 months" – a frequent response by the Obama campaign when questioned about the slow economic recovery.

The Associated Press and others point out that statement is misleading because it counts jobs from the recession's lowest point to where employment began to grow again – excluding jobs lost earlier in Obama's term and masking that overall unemployment has increased over that period.

"Overall, roughly 7.5 million jobs were lost during the recession that began in December 2007 and ended officially in June 2009," according to the wire service.

The Associated Press also points out that Obama said in his speech that he wants to use money saved by ending the wars to build highways, schools and bridges.

However, the wars were largely financed by borrowing "so there is no ready pile of cash to be diverted to anything else," the wire service writes.

The group FactCheck.org listed eight instances in which either Biden or Obama "spun" facts during their speeches Thursday night in Charlotte, N.C.

The group point out that Obama boasted that "independent experts" found his economic plan would cut the deficit by $4 trillion over 10 years. However, one such analyst called a key element of the plan a ‘gimmick,’ the group said.

Other examples include the president saying U.S. auto makers are back on top of the world.

"Nope," writes FactCheck, pointing out that General Motors has slipped back to No. 2 and is headed for third place in global sales this year behind Toyota and Volkswagen.

The group said Biden misquoted Mitt Romney when he said the GOP presidential nominee "believes it's OK to raise taxes on middle classes by $2,000."

FactCheck said it found just "a few bits of exaggeration and puffery" in the Romney speech, even citing a tweet by Bill Burton, a former Obama press secretary, saying likewise.

The group said Romney exaggerated about the loss of family income under Obama because some occurred 13 months he took office.

However, the group said Ryan, in his acceptance speeches, made "false claims" or gave “misleading statements” at least five times – among them were that president’s health care law funnels money away from Medicare “at the expense of the elderly.”

FactCheck pointed out Medicare’s chief actuary says the law "substantially improves" the system's finances and that Ryan has embraced the same savings.